I have an app called IPieta with a lot of great Catholic sources, (free app) including the Catechism of Thomas Aquinas.  Under the section on Baptism it says: 

ERRORS CONCERNING BAPTISM
There have been certain errors concerning this Sacrament. The first was that of the Solentiani, who received a baptism not of water but of the spirit. Against them the Lord says: “Unless a man be born again of water and the Holy Spirit, he cannot enter into the kingdom of God.”[15] 

...
So, if someone could persuade me that the sentence, "I cannot play baseball without a bat or a ball, since the coach said that I have to have a bat and a ball to play baseball," actually means that I can play baseball with EITHER a bat OR a ball, then you could convince me that Trent teaches BoD in this passage.

While the final draft used the phrasing, "cannot be effected without...", the preparatory draft used the phrasing, "is effected by", i.e. "this translation, since the promulgation of the gospel, is effected by the laver of regeneration, or the desire thereof."


Preparatory Draft

Quibus verbis huius, de qua sermo est justificationis descriptio continetur.  Est enim translatio ab eo statu, in quo homo nascitur filius primi adae in statum gratiae et adoptionis filiorum dei per secundum Adam Jesum Christum salvatorem nostrum: quae translatio post evangelium promulgatum lavacro regenerationis, aut eius voto efficitur, sicut scriptum est:  Nisi quis renatus etc.

--- Acta Authentica SS. Oecuмenici Concilii Tridentini, Tomus I, p.245-246
https://www.google.com/books/edition/Acta_genuina_Ss_oecuмenici_Concilii_Trid/LQ9jAAAAcAAJ?hl=en&gbpv=1  


Final Draft

Quibis verbis justification impii insinuator, ut sit translatio ab eo statu, in quo homo nascitur filius primi Adae, in statum gratiae et adoptionis filiorum dei per secundum Adam Jesum Christum salvatorem nostrum.  Quae quidem translatio post evangelium promulgatum, sine lavacro regenerationis, aut eius voto fieri non potest, sicut scriptum est: Nisi quis renatus...

--- pp.280-281